I had also posted a version of the paper on arXiv. The arXiv version of the paper and the journal's version are not identical, because the journal's version uses their house LaTeX style. However, the two versions are otherwise the same, and share the same theorem numbering.

Then someone pointed out an error in the paper. So I wrote a short correction, and submitted it to the journal. It has been accepted and published as a separate paper.

My question is: what should I do with the arXiv version of the paper? Here are some possibilities.

Replace the version on arXiv with a new version, which incorporates the necessary changes into the paper. Doing so would probably change the theorem numbering, so that it does not agree with the original paper.

Post the correction to the arXiv as a separate paper, and leave the old arXiv version of the original paper alone (so that it still agrees with the published version).

Post the correction to arXiv as a separate paper, and to replace the original paper on arXiv with a new version, which incorporates footnotes pointing out the erroneous statements, and referencing the correction (but otherwise not changing theorem numbering).

The third choice seems like the right one to me. But I'd like to know what the accepted practice is here (if there is one).

Added. Several answers suggest a fourth choice:

4. Replace the original paper on arXiv with a revised version, but make sure the revision does not change theorem numbering, or at least carefully indicate the changes in numbering.

Added. The consensus seems to be for choice 4. This is what I'll do, since it looks like I'll be able to keep the numbering the same.

References to arXiv papers should always include a version number, IMO (and arXiv should make it very prominent to the user when a version has been replaced---it could even make a watermark on the PS/PDF/etc files it generates for them) That makes your issue vanish in the air!
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Mariano Suárez-Alvarez♦Dec 11 '10 at 20:11

Option 1. It's one thing the arxiv is good for! There are probably several ways to keep the theorem numbering the same, depending on the precise nature of the changes you have to make.
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SheikraisinrollbankDec 11 '10 at 21:11

5

How about putting the corrections in an appendix?
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Thierry ZellDec 11 '10 at 22:31

5 Answers
5

In any case I think you should update the arXiv paper, that's where most people will read your paper anyways. Besides, writing a separate errata paper seems a bit unnecessary in this case. In the arXiv version you could probably add a footnote about the change of numbering.

On the other hand, when people reference a result our article, it would be convenient if the numbering is the same in both versions. Would it be possible to change the theorem numbering in the arXiv paper so that it resembles the submitted version?

Changing the numbering of theorems in the arXived version breaks all references to the paper which include a theorem number.
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Mariano Suárez-Alvarez♦Dec 11 '10 at 20:34

Yes, that is true. Although I don't think any significant confusion could arise from this. I think the important point is that the arXiv version, which is what google will see, should be the most updated version.
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J.C. OttemDec 11 '10 at 21:48

I'd be inclined to use option 1. If I correctly understand the arXiv's policies, the old version will remain available anyway. You could include in the new version a footnote indicating which arXiv version corresponds to the published version. If you're really worried about the changed theorem numbers, a "reader's guide" to the changes could be included either as a footnote in the new arXiv version or as an arXiv comment.

I agree. Go for option 1. If you are creative enough, there will be a way to incorporate the corrections without renumbering everything. Having a separate arXiv posting just for the "erratum" seems like overkill.
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Spiro KarigiannisDec 11 '10 at 20:11

6

I agree. Don't change the theorem numbering. There are all sorts of other options. But fix up the paper, don't just submit a "correction" to ArXiv. This is the whole point of living in the 21st century.
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Kevin BuzzardDec 11 '10 at 20:19

I agree with Option 1. The version on the arXiv should be self-contained as it will, I suspect, be the one that is actually read so making the arXiv version as simple to use as possible would be my priority here. I would also like to point out that there are lots of ways to "fix" the theorem numbering without it being too much of a headache so that theorems that are in both version are correctly labelled. I can think of one or two ways to do this, but I would recommend asking on tex.stackexchange.com about how to implement this.
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Loop SpaceDec 11 '10 at 21:01

You could post a new version where you have attached the correction to the paper (I thought this could be done automatically when updating papers on the arXiv?). This way, you keep the numbering, and people who look for the original paper will find the update as well.

I second this. I was in exactly the same situation, and have submitted the original version + errata in two separate TeX files as arXiv update, and they were happily and automatically combined in one pdf by arXiv. In fact, I was encouraged to do that after consultation with arXiv admins.
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Pasha ZusmanovichJan 4 '11 at 9:40

The theorem-numbering is irrelevant - re-write the paper and re-post on the ArXiv; the best version of your paper is then right there front and center. Old version are kept there as well, so if someone is reading a reference to the old version of your paper they can look it up easily enough (and if someone has been sloppy enough to reference an ArXiv paper without mentioning the version, well, shame on them).

I fear that most people will reference the PUBLISHED version and thus won't put a version number on their reference, so their readers won't expect anything to have changed. They will just google for the name of the article and download the first publicly avaliable google hit - i. e., the most recent arXiv version. Let's face the fact that USUALLY theorem numbers don't change when something is modified, so I think one should at least mention this pitfall in the introduction of the new version.
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darij grinbergDec 11 '10 at 21:58

Oh, sure - I'd definitely mention something in the intro. I see discrepancies between published work and some form of that work on the ArXiv as a pretty natural thing. I like to put a note on arxiv papers saying: "this is the version published in ___"; sometimes I have "alternate" versions or re-working of the material in newer arxiv posts, reflecting the fact that sometimes one's thinking on a topic evolves or errors are found or etc.
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Dr ShelloDec 11 '10 at 22:26

Probably there are also ways to force LaTeX to renumber the new theorems in such a way as it doesn't conflict with the old numbering. (Theorem 6.3B or something similar, or perhaps have the added theorems with their own numbering system using a different counter, roman numerals or something?)